Answer
$$ = {{105\,\sqrt{2}\,\ln \left(x^2+2\right)-342\sqrt{2}\, \ln \left(3\,x+2\right)+968\sqrt{2}\,\ln \left(3\,x+1 \right)-1020\,\arctan \left({{x}\over{\sqrt{2}}}\right)}\over{627\,2 ^{{{5}\over{2}}}}} $$
Explanation
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